Question

Find six rational numbers between 2/4 and 3/4
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Answer 1

The six rational numbers between  $\frac{2}{4}$ and $\frac{3}{4}$, are:$\frac{15}{28}, \frac{4}{7}, \frac{17}{28}, \frac{9}{14}, \frac{19}{28} , \frac{5}{7}$ .

To find six rational numbers between $\frac{2}{4}$ and $\frac{3}{4}$, we can divide the interval between these two fractions into equal parts and find the rational numbers within those intervals.

To find six rational numbers, we need to divide the interval between  $\frac{2}{4}$ and $\frac{3}{4}$ into seven equal parts (including the endpoints).

The difference between  $\frac{2}{4}$ and $\frac{3}{4}$ is $\frac{3}{4} -\frac{1}{2}= \frac{1}{4}$. Dividing this difference into seven equal parts gives us $\frac{1}{4} \div 7 = \frac{1}{28}$.

Starting from half , we can add multiples of the difference to find the six rational numbers between  $\frac{2}{4}$ and $\frac{3}{4}$,

The rational numbers are as follows:

$\frac{1}{2} + \frac{1}{28} = \frac{15}{28} \\\\\frac{1}{2} + \frac{2}{28} = \frac{4}{7} \\\\\frac{1}{2} + \frac{3}{28} = \frac{17}{28} \\\\\frac{1}{2} + \frac{4}{28} = \frac{9}{14} \\\\\frac{1}{2} + \frac{5}{28} =\frac{19}{28} \\\\\frac{1}{2} + \frac{6}{28}= \frac{5}{7}$

So, the six rational numbers between  $\frac{2}{4}$ and $\frac{3}{4}$, are:$\frac{15}{28}, \frac{4}{7}, \frac{17}{28}, \frac{9}{14}, \frac{19}{28} , \frac{5}{7}$ .

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